Using NMR chemical shifts as structural restraints in molecular dynamics simulations of proteins

We introduce a procedure to determine the structures of proteins by incorporating NMR chemical shifts as structural restraints in molecular dynamics simulations. In this approach, the chemical shifts are expressed as differentiable functions of the atomic coordinates and used to compute forces to generate trajectories that lead to the reduction of the differences between experimental and calculated chemical shifts. We show that this strategy enables the folding of a set of proteins with representative topologies starting from partially denatured initial conformations without the use of additional experimental information. This method also enables the straightforward combination of chemical shifts with other standard NMR restraints, including those derived from NOE, J-coupling, and residual dipolar coupling measurements. We illustrate this aspect by calculating the structure of a transiently populated excited state conformation from chemical shift and residual dipolar coupling data measured by relaxation dispersion NMR experiments.